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Use synthetic division to find .Write your answer in the form , where is a polynomial, is an integer, and is a linear polynomial. Simplify any fractions._________
Full solution
Q. Use synthetic division to find .Write your answer in the form , where is a polynomial, is an integer, and is a linear polynomial. Simplify any fractions._________
- Set up synthetic division: Set up synthetic division with as the root from and the coefficients of the polynomial , which are , , and .
- Perform synthetic division: Perform synthetic division: | | ---------------- The numbers on the bottom row are the coefficients of the quotient polynomial and the remainder.
- Write quotient polynomial: Write the quotient polynomial using the coefficients from the bottom row of the synthetic division. Since we started with a quadratic polynomial and divided by a linear polynomial, the quotient will be linear: .
- Remainder is : The remainder is , as seen in the last number on the bottom row of the synthetic division.
- Write final answer: Write the final answer in the form . Since the remainder is , the division is exact and there is no remainder term: .
